Possible Lifshitz point behaviour in NbO2

Seeded growth induced amorphous to crystalline transformation of niobium oxide nanostructures

A novel high-temperature synthesis of niobium oxide nanostructures has been developed through an amorphous intermediate that crystallizes into anisotropic crystalline structures through a complex mechanism of nucleation-dissolution-selective growth induced by seeded growth. The amorphous materials formed by the thermolysis of niobium oleate transformed into crystalline platelets, wires or bundled wires after the injection of additional niobium oleate at different temperatures. The temperature of the solution during injection of the additional precursor determined the morphology of the formed crystalline structure. The time- and temperature-dependent evolution of the niobium oxide nanostructures demonstrates that amorphous materials progressively turned to crystalline materials. We tuned the size of wires and platelets by the consecutive injection of the precursor solution into the reaction mixture under isothermal conditions. With the sequential injection of the precursor solution, we demonstrate that the anisotropic growth of individual nanowires occurs exclusively along the ends, without the formation of any new nuclei. A mechanism for the transformation of well-defined platelets from wires has been proposed and is due to the exclusive loss of mass at the ends of the wires while growth of the platelets initially occurs along the (001) direction which is then replaced by the (110) face.

Unusual symmetries in the Kugel-Khomskii Hamiltonian

The Kugel-Khomskii Hamiltonian for cubic titanates describes spin and orbital superexchange interactions between d(1) ions having threefold degenerate t(2g) orbitals. Since orbitals do not couple along "inactive" axes, perpendicular to the orbital planes, the total number of electrons in |alpha> orbitals in any such plane and the corresponding total spin are both conserved. A Mermin-Wagner construction shows that there is no long-range spin ordering at nonzero temperatures. Inclusion of spin-orbit coupling allows such ordering, but even then the excitation spectrum is gapless due to a continuous symmetry. Thus, the observed order and gap require more symmetry breaking terms.